WO2012174098A2 - Découplage dynamique dans des ensembles de spin à semi-conducteur - Google Patents

Découplage dynamique dans des ensembles de spin à semi-conducteur Download PDF

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Publication number
WO2012174098A2
WO2012174098A2 PCT/US2012/042232 US2012042232W WO2012174098A2 WO 2012174098 A2 WO2012174098 A2 WO 2012174098A2 US 2012042232 W US2012042232 W US 2012042232W WO 2012174098 A2 WO2012174098 A2 WO 2012174098A2
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spin
impurities
pulse sequence
pulses
ensemble
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WO2012174098A3 (fr
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Ronald Walsworth
My PHAM
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Harvard University
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Harvard University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
    • G01R33/32—Excitation or detection systems, e.g. using radio frequency signals
    • G01R33/323—Detection of MR without the use of RF or microwaves, e.g. force-detected MR, thermally detected MR, MR detection via electrical conductivity, optically detected MR
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/60—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using electron paramagnetic resonance
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N24/00—Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects
    • G01N24/08—Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects by using nuclear magnetic resonance
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/24—Arrangements or instruments for measuring magnetic variables involving magnetic resonance for measuring direction or magnitude of magnetic fields or magnetic flux

Definitions

  • the negatively-charged nitrogen-vacancy (NV) color center in diamond possesses many useful properties, including without limitation: long electronic spin coherence times at room temperature; optical mechanisms for initializing and detecting their spin states; and electron spin resonance (ESR) techniques that allow for coherent spin manipulation.
  • the NV color center has generated much interest for scalable applications in quantum information and metrology, such as sensitive detection of electric and magnetic fields.
  • FIG. 1 is a schematic block diagram of a system for implementing multi-pulse dynamical decoupling of an ensemble of NV centers in diamond.
  • FIG. 2A illustrates an NV color center in a diamond lattice.
  • FIG. 2B illustrates the energy level structure of negatively charged NV center shown in FIG. 2A.
  • FIG. 3 illustrates a number of different spin control pulses that can be used for dynamic decoupling of multi-spin ensembles, in accordance with some embodiments of the present application.
  • FIG. 4 plots the measurements of NV multi-spin coherent evolution using an w-pulse CPMG control sequence, for a diamond sample having an NV density of ⁇ 60 ppb, and a spin-bath environment consisting of 100 ppm nitrogen atoms (N), and 1.1 % concentration of
  • FIG. 5 illustrates examples of measured normalized fluorescence signals as functions of AC field magnitude B ac using a Hahn Echo sequence and multi-pulse XY sequences with different numbers of control pulses.
  • FIG. 6 provides a comparison of calculated and measured AC magnetic field sensitivity, using dynamical decoupling control pulses.
  • FIG. 1 is a schematic block diagram of a system 100 for implementing multi-pulse dynamical decoupling of solid-state multi-spin systems, which in the illustrated embodiment is an ensemble of NV centers in room temperature diamond.
  • multi-pulse dynamical decoupling may be performed on solid-state multi-spin systems other than NV centers in diamond, including without limitation phosphorous donors in silicon.
  • the system 100 is a wide-field fluorescence microscope.
  • the system 100 includes a pulsed microwave source 130 configured to generate a series of microwave control pulses and apply them to a sample 1 10.
  • the microwave source 130 is a loop antenna designed to generate a homogeneous Bj field over the sample detection volume, thereby generating resonant microwave control pulses for coherent manipulation of the NV spin states.
  • the sample 1 10 is a diamond crystal containing an ensemble of NV centers.
  • the spin-bath environment comprises l3 C (carbon 13) nuclear spin impurities and N (nitrogen atom) electronic spin impurities.
  • the diamond samples may consist of an NV-rich layer grown by chemical vapor deposition on a non-fluorescing diamond substrate.
  • the sample 100 may include an ensemble of spin impurities having a density of at least about 10 l 2 /cm 3 .
  • the optical source 120 is a switched 3-Watt 532-nm laser that can provide optical excitation of NV centers within a 10 //m-diameter cross-section of each sample.
  • An AOM (acousto-optic modulator) 132 for example an Isomet M l 133-aQ80 L-H, pulses the excitation laser 120 with precise timing in order to prepare and read out the NV spin states.
  • the system 100 further includes a detector 140 configured to detect output optical radiation from the spin impurities after being exposed to the optical excitation signal and the series of microwave control pulses.
  • the detector 140 may be an optical fluorescence detector, for example. Many other types of detectors may be used, including without limitation CCD (charge coupled device) arrays and photodiodes.
  • NV spin state-dependent fluorescence is collected by a microscope objective 122, and is imaged onto the optical fluorescence detector 140 after being separated from the excitation beam by a dichroic mirror 124 and filtered by red filters 128.
  • An optical chopper 126 is synched such that the initialization pulse is blocked from the detector 140, while the readout pulse is recorded.
  • the optical signal is shuttered by the optical chopper 126, allowing spatially resolved ensemble measurements.
  • a processing system may be integrated with the system 100 described in FIG.1.
  • the processing system is configured to implement the methods, systems, and algorithms described in the present application.
  • the processing system may include, or may consist of, any type of microprocessor, nanoprocessor, microchip, or nanochip.
  • the processing system may be selectively configured and/or activated by a computer program stored therein. It may include a computer-usable medium in which such a computer program may be stored, to implement the methods and systems described above.
  • the computer-usable medium may have stored therein computer-usable instructions for the processing system.
  • FIG. 2A schematically illustrates the crystal structure of an NV center 200 in a diamond lattice.
  • the NV center is an empty position or vacancy resulting from a missing carbon atom in the diamond lattice.
  • the NV impurity is based in the lattice of carbon atoms 210, where two adjacent sites are altered, because one carbon atom is replaced with a nitrogen atom 220 and the other space is left vacant.
  • the vacancies may interact with interstitial atoms such as nitrogen 220, and may act as color centers by absorbing visible light.
  • NV centers are visible as red spots when illuminated by laser. Applying a static field (Bo ⁇ 70 Gauss) along one of the four diamond crystallographic axes selected approximately one quarter of the NV centers to be resonant with the microwave pulses.
  • FIG. 2B shows the electronic structure of an NV center in diamond.
  • FIG. 3 illustrates some examples of spin control pulses for dynamic decoupling of multi-spin systems, in one or more embodiments of the present application.
  • An AC magnetic field b(t) is applied, where b(t) has a time dependence represented by:
  • phase ⁇ is chosen such that the nodes of the AC magnetic field b(t) coincide with the microwave ⁇ pulses.
  • the Hahn Echo, CPMG-2, CPMG-N, and XY-N control pulse sequences are shown.
  • the Hahn Echo sequence decouples NV spins from bath field fluctuations that are slow compared to the free precession time.
  • these additional control pulses are applied to large ensembles of NV spins, resulting in dynamic decoupling of the NV spins from magnetic field fluctuations that are slow compared to the time between the pulses.
  • FIG. 4 plots the measurements of NV multi-spin coherent evolution using an w-pulse CPMG control sequence, for a diamond sample having an NV density of ⁇ 60 ppb (as measured by NV fluorescence intensity), an N concentration of about ⁇ 100 ppm (measured by secondary ion mass spectroscopy), and ⁇ 1.1% natural abundance , 3 C concentration.
  • the high N concentration dominated NV decoherence in this sample, limiting the measured Hahn Echo multi-spin coherence time to Ti - 2 ⁇ s.
  • the diamond sample used in the measurements illustrated in FIG. 4 is an NV-rich layer with a thickness of about 16 ⁇ .
  • CPMG-n sequences were applied to the sample, and the NV multi-spin coherence time was determined as a function of the number of pulses.
  • T n) was determined from the Me decay of the spins' coherent evolution as a function of the total CPMG-H evolution period.
  • dynamical decoupling as described above can be applied to improve the sensitivity of N V multi-spin magnetometry.
  • the field amplitude bac can be extracted from the measurement of accumulated NV spin phase with optimum sensitivity, where an approximate expression for the sensitivity is given by:
  • C is a parameter that encompasses the measurement contrast, optical collection efficiency, and number of NV spins contributing to the measurement.
  • the contrast is modified by N V decoherence over the course of the measurement, described phenomenologically by an exponential factor with power p.
  • the value of p is found to be sample dependent, in the range of 1 to 2.5, and is related to the dynamics of the spin environment and to ensemble inhomogeneous broadening.
  • the AC magnetic field sensitivity was measured for a 30 ⁇ 3 sensing volume of a diamond sample with NV ⁇ 0.6 ppb and N ⁇ 1 ppm, with ⁇ 10 3 sensing NV spins.
  • FIG. 5 illustrates examples of measured normalized fluorescence signals as functions of AC field magnitude b m using a Hahn Echo sequence, and using multipulse XY sequences with 28 and 54 control pulses. As seen in FIG. 5, the uncertainty in the measured signal ( ⁇ 55) limits the uncertainty in the extracted magnetic field magnitude ( ⁇ B).
  • the sine behavior of the signal with respect to b ac is achieved by shifting the phase of the last microwave pulse by 90° from what is shown in FIG. 3.
  • FIG. 6 provides a comparison of calculated (lines) and measured (points) sensitivity, at several AC magnetic field frequencies.
  • NV multi-spin measurements confirm that multi-pulse dynamical decoupling outperform the Hahn Echo scheme over a wide range of AC magnetic field frequencies, in agreement with theoretical expectations.
  • the enhancement in magnetic field sensitivity provided by multi-pulse dynamical decoupling is especially pronounced at frequencies higher than the Hahn Echo 1/ 71 ⁇ 2 coherence.
  • Multi-pulse dynamical decoupling sequences have been disclosed that can extend the coherence lifetime of large numbers of NV electronic spins in room temperature diamond, by about an order of magnitude, for samples with widely differing N V densities and spin environments.
  • NV multi-spin coherence time greater than about 2 ms can be realized. This is comparable to the best results from application of dynamical decoupling to single NV centers. Multi-pulse dynamical decoupling improves NV multi-spin AC magnetic field sensitivity relative to the Hahn Echo scheme, with about a ten-fold enhancement for higher frequency fields.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Condensed Matter Physics & Semiconductors (AREA)
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  • Life Sciences & Earth Sciences (AREA)
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  • Investigating, Analyzing Materials By Fluorescence Or Luminescence (AREA)
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Abstract

Selon l'invention, des durées de vie de cohérence de spin longues sont obtenues pour des ensembles d'impuretés de spin électroniques dans des systèmes de spin à semi-conducteur, par exemple des centres de couleur NV dans un diamant, à l'aide de séquences d'impulsions RF à commande de spin pour fournir un découplage dynamique des ensembles d'impuretés de spin à partir de sources environnementales de décohérence telles que des interactions dipolaires et hyperfines avec un spin proximal et d'autres impuretés paramagnétiques dans un diamant. De cette façon, la sensibilité de mesure de l'évolution cohérente d'ensembles d'impuretés de spin à semi-conducteur est diminuée. A l'aide de la séquence d'impulsions Carr-Purcell-Meiboom-Gill (CPMG), les durées de vie de cohérence de spin d'ensembles NV peuvent être étendues à plus de 2 ms dans un diamant à température ambiante et la sensibilité de magnétométrie qui utilise des ensembles NV peut être augmentée.
PCT/US2012/042232 2011-06-13 2012-06-13 Découplage dynamique dans des ensembles de spin à semi-conducteur Ceased WO2012174098A2 (fr)

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US20150048822A1 (en) 2015-02-19
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